7 mark for review the derivative of the function f is given by f(x)=-3x + 4 for all x, and f(-1)=6. which of…

Explanation:

Step1: Find the slope of the tangent line

The slope of the tangent line to the graph of $y = f(x)$ at a point $x=a$ is given by $f^{\prime}(a)$. Here, $a=-1$ and $f^{\prime}(x)=-3x + 4$. So, $f^{\prime}(-1)=-3\times(-1)+4=3 + 4=7$.

Step2: Find a point on the tangent line

We know that $f(-1) = 6$, so the point $(-1,6)$ lies on the graph of $y = f(x)$ and also on the tangent - line.

Step3: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. Here, $x_1=-1$, $y_1 = 6$ and $m = 7$. Substituting these values into the point - slope form, we get $y-6=7(x + 1)$.

Step4: Simplify the equation

Expand the right - hand side: $y-6=7x+7$. Then, add 6 to both sides to get $y=7x + 13$.

Answer:

D. $y = 7x+13$